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The bar graph shows the average annual spending per person on selected items in 1980 and 2010. All dollar amounts are adjusted for inflation. Use this display to solve Exercises 33–34.In this exercise, we refer to annual spending per person in $1980 .$ The combined spending on housing, vehicles/gas, and health care was $\$ 7073 .$ The difference between spending on housing and spending on vehicles/gas was $\$ 1247$ . The difference between spending on housing and spending on health care was $\$ 1466$ . Find the average per-person spending on housing, vehicles/gas, and health care in $1980 .$

Thus, the amount spent in housing is $\$ 3262$ the amount spent in vehicles/gas is $\$ 2015$ the amount spent in health care is $\$ 1796$

Algebra

Chapter 7

Systems of Equations and Inequalities

Section 2

Systems of Linear Equations in Three Variables

Equations and Inequalities

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in this question, we want to translate the expenditures, the respective spending into three equations so that we can solve the equations simultaneously to find each expenditure. So let's translate the the different types off expended journalists that, in the question to three unknowns first. So if you're you're further a bar graph in the question we have housing represented by X vehicle against represented by why and health care represented by easy. So how to reform all three equations? We can get hints from the question. So, firstly, the question mentioned that the total expenditure IHS person amount so that forms our first equation by summing all of them. And then the question also mentioned the difference between, um, the spending on housing and spending on vehicle guests. So that's all second equation, and then the third equation is the difference between the spending on housing and the spending on health care. So that's keep, um, this bear in mind the three equations and let's work on the let's work on them by our through addition or subtraction to try to isolate and unknown to find its value. So there are many ways you can do this, but I'm gonna start off this equation one and two. So I'm gonna subject equation two from Equation one. How I do this is by having the left hand side off. Equation one minus the left hand side of equation two equals to the right hand side of equation one minus the right hand side off equation too. And in the wind. So I eliminate the unknown X. And now I have in the equation with just y and Z. So this my equation for I'm gonna do it again with Equation two and three by having the left inside of equation to minus left inside, off equation three equals to the right hand side of equation three minus the right hand side off equation off three equal. Do the right hand side off equation to minors. The right hand side off equation three. And this is my fifth equation. So now you Christians four and five have on Lee y and Z, and I'm gonna extend this process to illuminate another unknown to find. And in this case, I'm eliminating Z so I can find the value off why and with the value off, why I can substitute it back into IDA equation four or five to sign the value off Z. So in this case of Children to work with equation five to find the value off Z, you should be able to get the same answer. If you use equation for and with both y and Z values, I can substitute them back into any off the 1st 3 equations to find the value off X. So in this case, have Children toe what with Equation two. But again, you should be able to get the same and the regardless off which equation you choose. We got those, whether it's equation one or two off three.

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