# Question Video: Solving a Linear System of Equations Graphically Mathematics • 8th Grade

Use the shown graph to solve the given simultaneous equations. 𝑦 = 4𝑥 − 2, 𝑦 = −𝑥 +3

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### Video Transcript

Use the shown graph to solve the given simultaneous equations. 𝑦 equals four 𝑥 minus two and 𝑦 equals negative 𝑥 plus three.

Firstly, we notice that the graph we have been given is the graph of the two straight lines represented by these equations. Considering the blue line, first of all, we see that it has a 𝑦-intercept of three and a slope of negative one. So, substituting these values into the general equation of a straight line in its slope–intercept form, we can see that the equation of the blue line is 𝑦 equals negative 𝑥 plus three. That’s the second of the two equations we were given.

In the case of the green line, we see that it has a 𝑦-intercept of negative two and a slope of four. So, substituting these values into the general equation of a straight line, we find that the equation of this line is 𝑦 equals four 𝑥 minus two. That’s the first equation that we were given.

So, this figure represents these two equations graphically, and we can therefore use it to solve them simultaneously. The solution to this pair of linear simultaneous equations will be the coordinates of the point that lies on both lines. That is the point where the two lines intersect. We can see from the graph that the lines intersect at this single point here. And it’s a point with integer coordinates. The 𝑥-coordinate is one, and the 𝑦-coordinate is two. The solution to this pair of simultaneous equations, then, is 𝑥 equals one and 𝑦 equals two.

We could, of course, check this by substituting this pair of 𝑥-, 𝑦-values into each equation and confirming that they do indeed satisfy each equation. Although we can see quite clearly from our graph that this point does lie on both lines.